Statistical Foundations of Liquid-Crystal Theory. I: Discrete Systems of Rod-Like Molecules

We develop a mechanical theory for systems of rod-like particles. Central to our approach is the assumption that the external power expenditure for any subsystem of rods is independent of the underlying frame of reference. This assumption is used to derive the basic balance laws for forces and torques. By considering inertial forces on par with other forces, these laws hold relative to any frame of reference, inertial or noninertial. Finally, we introduce a simple set of constitutive relations to govern the interactions between rods and find restrictions necessary and sufficient for these laws to be consistent with thermodynamics. Our framework provides a foundation for a statistical mechanical derivation of the macroscopic balance laws governing liquid crystals.     

Two Years of Pesticides Monitoring in a Belgian Watershed

A monitoring study was carried out in 1998-1999 on a medium-sized (c. 4580 km²) watershed of the Dyle (or Dijle) river in central Belgium, composed of both rural and urbanized areas. This watershed may be considered as representative of a large part of the country. Samples were taken each month from seven sites along the course of the river, plus one from its major affluent the Demer. The eight molecules monitored were the main herbicides used on the major crops in the area, plus some used in nonagricultural sectors. The concentrations found were mostly in the 0-3 μg/L range, with some peaks between 3 and 14 μg/L. The averages over all spring and summer samples analyzed ranged from 0.14 (bentazone) to 1.54 μg/L (diuron). Time and space specific patterns could be observed.     

Statistical Foundations of Liquid-Crystal Theory II: Macroscopic Balance Laws

Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media.     

Synthetic Applications of Phosphonium Diylides

Abstract

Phosphonium diylides 1 react with electrophiles leading to new monoylides which permit., by a Wittig reaction, the E stereoselective synthesis of various di- or tri-substituted α,β-unsaturated functionalized compounds.     

Nonreciprocal devices in integrated optics

This article reviews the solutions that have been studied for the implementation of nonreciprocal devices in integrated optics. These components, either isolators or circulators, use the nonreciprocal interaction between light and a magnetic medium. The only two isolators that have been experimented on to date are described in detail with their advantages and drawbacks, and some solutions are proposed to overcome the difficulties encountered.     

Stereospecific Synthesis and Acylation of cis 1-Halo 2-Trimethylsilyl Ethylenes

Several routes to 1-halo 2-trimethylsilyl ethylenes have been previously proposed ^1-6: from ethyn7yltrimethylilane (addition of HBr^1,2), ethyltrichlorosilane (addition H by C1, followed by dehydrohalogenation and further methylation of th Si-C1 bonds)³ or by other ways ^4,5, especially by reaction of (2-trimethylsilyl) vinyl lithium with dibromoethane⁶.     

Influence of benzo-bridging on the stability of 6aλ4-thia-1,2,5,6-tetraazapentalenic systems

Methylation of the phenylhydrazone derived from 8-oxo-8H-indeno[1,2-d]-1,2,3-thiadiazole 5 with Meerwein's reagent furnishes the two methylated products 7 and 8. Single crystal X-ray analyses of these compounds reveal no significant S…NPh interaction, thus excluding a thiapentalene structure.     

FT-IR and FT-FIR studies of vanadium,molybdenum and tungsten oxides supported on different carriers

In the far IR region at low molybdenum loadings, Mo-SiO₂ catalysts present a pseudomolybdate or a polymolybdate species, while bulk-like MoO₃ appears at loadings close to the geometrical monolayer coverage. W-SiO₂ and V-SiO₂ spectra show bands close to those observed on the corresponding bulk oxides.In the case of TiO₂, Al₂O₃, ZrO₂ supported catalysts, a band is observed near 1000 cm^–1 which is assigned to the Mo=O stretching vibration of coordinatively unsaturated Mo ⁿ⁺ ions showing a stronger interaction with the support than one observed on silica.